Question

What is the function rule for these ordered pairs (-2, 10) (-1, -7) (0, -4) (1, -1) (2, 2)?

Answer 1

`color(blue)("So the function rule is "y=3x-4)`

Explanation:

Given:
`y-> 10;-7;-4;-1;2`
`x->-2;-1;0;1;2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Assumption: the question has an error. The +10 should be -10

Thus we have

`y_2-y_1 -> -7-(-10) = +10-7 = +3`

`"-10 -7 -4 -1 2"`
`" \/"color(white)(.)"\ /"color(white)(.)"\/"color(white)(.)"\/"`
`" 3 3 3 3 " larr " difference in "y" (increasing)"`

`"-2 -1 0 1 2"`
`" \/"color(white)(.)"\ /"color(white)(.)"\/"color(white)(.)"\/"`
`" 1 1 1 1 " larr " difference in "x" (increasing")`

'~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the standard form equation of a straight line:
`" "y=mx+c`

where m is the gradient `->( "change in y")/("change in x") -> (+3)/(+1)=+3`

`y=3x+c`

Take any given point `P->(x,y)" " -> (-1,-7)`

Then `y=3x+c" " ->" "-7=3(-1)+c`

`=> c = 3-7=-4`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("So the function rule is "y=3x-4)`